Elliptic curve isogeny class with Cremona label 8670e (LMFDB label 8670.g)

• Label: 8670e
• Number of curves: $8$
• Conductor: $8670$
• CM: no
• Rank: $0$

Elliptic curves in class 8670e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8670.g8	8670e1	$[1, 1, 0, 428, 10624]$	$357911/2160$	$-52137149040$	$[2]$	$9216$	$0.73832$	$\Gamma_0(N)$-optimal
8670.g6	8670e2	$[1, 1, 0, -5352, 134316]$	$702595369/72900$	$1759628780100$	$[2, 2]$	$18432$	$1.0849$
8670.g7	8670e3	$[1, 1, 0, -3907, -309299]$	$-273359449/1536000$	$-37075305984000$	$[2]$	$27648$	$1.2876$
8670.g5	8670e4	$[1, 1, 0, -19802, -932094]$	$35578826569/5314410$	$128276938069290$	$[2]$	$36864$	$1.4315$
8670.g4	8670e5	$[1, 1, 0, -83382, 9232614]$	$2656166199049/33750$	$814642953750$	$[2]$	$36864$	$1.4315$
8670.g3	8670e6	$[1, 1, 0, -96387, -11536371]$	$4102915888729/9000000$	$217238121000000$	$[2, 2]$	$55296$	$1.6342$
8670.g1	8670e7	$[1, 1, 0, -1541387, -737215371]$	$16778985534208729/81000$	$1955143089000$	$[2]$	$110592$	$1.9808$
8670.g2	8670e8	$[1, 1, 0, -131067, -2540379]$	$10316097499609/5859375000$	$141431068359375000$	$[2]$	$110592$	$1.9808$

Rank

The elliptic curves in class 8670e have rank $0$.

Complex multiplication

The elliptic curves in class 8670e do not have complex multiplication.

Modular form 8670.2.a.e

Isogeny matrix

The $i,j$ entry is the smallest degree of a cyclic isogeny between the $i$-th and $j$-th curve in the isogeny class, in the Cremona numbering.

$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.